Suggested correction, hope that it helps!

Carol and Ted

It was a beautiful Sunday morning. The weather was sunny and warm. So Carol decided to walk down the street.

There were only a few people outside, so the walk was enjoyable. Passing by a small restaurant, she noticed the menu in the window.

Carol started reading it because she was hungry and didn't mind having something as a snack.
The menu was so inspiring, There were nice dishes and at reasonable prices, and as the menu was so inspiring, she couldn't help but come go in. Carol ordered spaghetti Bolognese which and thought it was delicious.

At the same time, Ted was also at the restaurant. Carol's blond hair and blue eyes had caught his attention just when just as she entered the restaurant.
When Carol finished eating and left Ted could not accept the fact that he was couldn't believe that he had been such a coward. "What a pity! I would never meet shame! I'm never going to see her again," he thought. But a moment later, he noticed that she had left her bag on the chair. He grabbed it and ran out. He saw Carol getting into a taxi. It was too late. Ted got disappointed but found her address in the wallet inside bag after a while he found her address in the bag \ in her wallet\. What good luck!

Coming\ Approaching her house, Ted he was so nervous that he couldn't find the right words to start the conversation. Taking a deep breath, \having taken a deep breath\ he rang the bell. holding the bag in front of him. Carol opened the door and was pleasantly surprised \gasped in amazement\. So She couldn't find the right words either! In gratitude  To thank him    To thank him, she invited Ted in for a cup of tea. They laughed a lot on that day and long after as well.

They fell in love with each other and got married. The only person who cried in the story was the waiter because Carol hadn't paid before leaving the restaurant.

Mostly very minor corrections --  the flow is very natural and the grammar is quite strong, so it was simply a question of adding some finesse to a few sentences here and there!